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Proof of a conjecture on the genus two free energy associated to the An singularity
Journal of Geometry and Physics,2014,76():10-24 | 2014年02月01日 | https://doi.org/10.1016/j.geomphys.2013.10.013
In a recent paper Dubrovin et al. (1998), it is proved that the genus two free energy of an arbitrary semisimple Frobenius manifold can be represented as a sum of contributions associated with dual graphs of certain stable algebraic curves of genus two plus the so called genus two G-function, and for a certain class of Frobenius manifolds it is conjectured that the associated genus two G-functions vanish. In this paper, we prove this conjecture for the Frobenius manifolds associated with simple singularities of type A.
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